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Phase integral theory, coupled wave equations, and mode conversion.

Robert G. Littlejohn¹, William G. Flynn

¹Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720.

Chaos (Woodbury, N.Y.)

|January 1, 1992

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Phase integral, or WKB theory, is applied to complex wave equations. This method simplifies analysis of multicomponent wave fields, aiding in understanding mode conversion and Landau-Zener-Stuckelberg transitions in multidimensional systems.

Area of Science:

Mathematical Physics
Quantum Mechanics
Physical Chemistry

Background:

WKB theory is a semiclassical method for approximating solutions to differential equations.
Multicomponent wave equations describe complex physical systems like coupled channels in scattering.
Mode conversion, including Landau-Zener-Stuckelberg transitions, is crucial in various physical phenomena.

Purpose of the Study:

To extend the application of phase integral (WKB) theory to multicomponent wave equations.
To analyze the specific case of coupled channel equations in atomic and molecular scattering.
To investigate multidimensional mode conversion and its group-theoretical underpinnings.

Main Methods:

Application of phase integral (WKB) theory to vector, spinor, and tensor wave fields.

Related Experiment Videos

Analysis of coupled channel equations within the Born-Oppenheimer approximation.

Casting multidimensional mode conversion into a normal form using group theory.

Main Results:

Demonstration of WKB theory's applicability to complex multicomponent wave equations.
Identification of simplified analysis for specific physical systems like coupled channels.
Formulation of multidimensional mode conversion in normal form, revealing connections to Lorentz and symplectic groups.

Conclusions:

Phase integral (WKB) theory provides a powerful framework for analyzing multicomponent wave equations.
The study offers new insights into mode conversion phenomena, particularly Landau-Zener-Stuckelberg transitions.
Group theoretical principles, involving Lorentz and symplectic groups, are essential for understanding normal form transformations in these systems.